Stephen,
your observation is correct, of course, and it does make the IVP-of relation look not well-behaved, but that's because the temporal
interval that defines Bobs validity explicitly, has remained "hidden" in the def. of IVP-of relation, while it should have been
made explicit there, as well.
So if you add your sentence "B IPVof A is defined to only hold over the temporal intersection of A and B" to the def. of IVP-of
(as we should have done as it makes no sense to establish a relation between two Bobs, one of which is out of scope), then over this
restricted interval the relation /is/ transitive, right?
What I mean is that the problem is not that IVP-of is not transitive, but that in the def. we omitted to qualify the scope within
which the relation itself holds.
Regarding better-behaved relations, personally (and bear in mind this is not /my/ def.) I rather like the general case in which
- the set of attributes overlap (with no strict set containment requirement)
- the temporal scopes overlap (with no strict interval containment requirement)
as these conditions lead, within a possibly restricted scope, to an equivalence relation. That said, whether this is still
practically useful is a separate issue...
-Paolo
On 7/28/11 1:13 PM, Cresswell, Stephen wrote:
>
> Paolo,
>
> I donâ€™t see how IVPof can be usefully considered transitive in its current definition, as I think it would be possible for some
> transitively-derived IVPof relations to be valid only over empty time intervals. This is because B IPVof A is defined to only
> hold over the temporal intersection of A and B, but the relation of having non-empty temporal intersection is itself not transitive.
>
> For example, we can have three time intervals X, Y, Z such that X overlaps Y, Y overlaps Z, but X is disjoint from Z.
>
> Then if we have bobs Bx, By, Bz which hold over the respective time intervals, and we asserted
>
> Bx IVPof By
>
> By IVPof Bz
>
> â€¦ then transitivity would allow us to derive
>
> Bx IVPof Bz
>
> â€¦ but that is dubious because it would hold only over the temporal intersection of X and Z, which is empty.
>
> I was hoping that the definition of B IVPof A would turn out to require that the time interval of B was contained in the time
> interval of A. I think that would be a simpler and better-behaved relation, which should be glorified with a name, even itâ€™s not
> â€œIVPofâ€